This invention relates to a racing game in which playing pieces are moved along a track in response to random generation of movement information, and each player receives a score according to scoring data at a storage location that corresponds to the order in which the piece assigned to that player crosses a finish line. In particular, the invention relates to a racing game in which the scoring data stored at each storage location consists of value markers contributed by the players during the game in response to triggering events that require the players to select a storage location and to store a value marker at that location. The winner is not necessarily the player whose piece finishes first but the one who receives the highest score.